Question

The equilibrium constant K_c for the decomposition of phosgene,

COCl₂,

is

4.63

×

10⁻³

at 527

°

C:

COCl₂(g) ⇆ CO(g) + Cl₂(g)

Calculate the equilibrium partial pressure of all the components, starting with pure phosgene

at 0.460 atm.

PCOCl2

=

PCO

=

PCl2

=

Answer 1

Solution-

Assuming 1 L volume

Applying formula
n = PV/RT

putting the value-

= 0.460 atm x 1 / 0.08206 x 800 K
n = 0.007 mole/L

Now,
Kc = [CO][Cl2][ / [COCl2]
let us assume[CO] = [Cl2] = X
[COCl2] = 0.007 - X
4.63x10^-3 = X^2 / (0.007 - X)

=>0.000032-4.63*10^-3X=X^2

=>X^2+4.63*10^-3-0.000032=0

SOLVING THIS QUADRATIC EQUATION

X = 0.0038 mol
[CO] = 0.0038 mol
[Cl2] = 0.0038 mol
[COCl2] = 0.0032 mol
total moles = 0.0108
P total = 0.760 atm x (0.0108 / 0.007)

= 1.172 atm
partial pressure CO = 0.249 atm
partial pressure Cl2 = 0.249 atm
partial pressure COCl2 = 0.210 atm
Kp = (0.249)^2 / 0.210 = 0.295
Kc x RT = 4.63x10^-3 x 0.08206 x 800 = 0.304